3,105 research outputs found
Snapshot Observation for 2D Classical Lattice Models by Corner Transfer Matrix Renormalization Group
We report a way of obtaining a spin configuration snapshot, which is one of
the representative spin configurations in canonical ensemble, in a finite area
of infinite size two-dimensional (2D) classical lattice models. The corner
transfer matrix renormalization group (CTMRG), a variant of the density matrix
renormalization group (DMRG), is used for the numerical calculation. The matrix
product structure of the variational state in CTMRG makes it possible to
stochastically fix spins each by each according to the conditional probability
with respect to its environment.Comment: 4 pages, 8figure
Spin-charge separation in two-component Bose-gases
We show that one of the key characteristics of interacting one-dimensional
electronic quantum systems, the separation of spin and charge, can be observed
in a two-component system of bosonic ultracold atoms even close to a competing
phase separation regime. To this purpose we determine the real-time evolution
of a single particle excitation and the single-particle spectral function using
density-matrix renormalization group techniques. Due to efficient bosonic
cooling and good tunability this setup exhibits very good conditions for
observing this strong correlation effect. In anticipation of experimental
realizations we calculate the velocities for spin and charge perturbations for
a wide range of parameters
High order non-unitary split-step decomposition of unitary operators
We propose a high order numerical decomposition of exponentials of hermitean
operators in terms of a product of exponentials of simple terms, following an
idea which has been pioneered by M. Suzuki, however implementing it for complex
coefficients. We outline a convenient fourth order formula which can be written
compactly for arbitrary number of noncommuting terms in the Hamiltonian and
which is superiour to the optimal formula with real coefficients, both in
complexity and accuracy. We show asymptotic stability of our method for
sufficiently small time step and demonstrate its efficiency and accuracy in
different numerical models.Comment: 10 pages, 4 figures (5 eps files) Submitted to J. of Phys. A: Math.
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Finite Temperature Density Matrix Renormalization using an enlarged Hilbert space
We apply a generalization of the time-dependent DMRG to study finite
temperature properties of several quantum spin chains, including the frustrated
model. We discuss several practical issues with the method, including
use of quantum numbers and finite size effects. We compare with transfer-matrix
DMRG, finding that both methods produce excellent results.Comment: 4 pages and 4 figure
Explicit solution of the Lindblad equation for nearly isotropic boundary driven XY spin 1/2 chain
Explicit solution for the 2-point correlation function in a non-equilibrium
steady state of a nearly isotropic boundary-driven open XY spin 1/2 chain in
the Lindblad formulation is provided. A non-equilibrium quantum phase
transition from exponentially decaying correlations to long-range order is
discussed analytically. In the regime of long-range order a new phenomenon of
correlation resonances is reported, where the correlation response of the
system is unusually high for certain discrete values of the external bulk
parameter, e.g. the magnetic field.Comment: 20 Pages, 5 figure
Atomic lattice excitons: from condensates to crystals
We discuss atomic lattice excitons (ALEs), bound particle-hole pairs formed
by fermionic atoms in two bands of an optical lattice. Such a system provides a
clean setup to study fundamental properties of excitons, ranging from
condensation to exciton crystals (which appear for a large effective mass ratio
between particles and holes). Using both mean-field treatments and 1D numerical
computation, we discuss the properities of ALEs under varying conditions, and
discuss in particular their preparation and measurement.Comment: 19 pages, 15 figures, changed formatting for journal submission,
corrected minor errors in reference list and tex
Applying Compactness Constraints to Seismic Traveltime Tomography
Tomographic imaging problems are typically ill-posed and often require the use of regularization techniques to guarantee a stable solution. Minimization of a weighted norm of model length is one commonly used secondary constraint. Tikhonov methods exploit low-order differential operators to select for solutions that are small, flat, or smooth in one or more dimensions. This class of regularizing functionals may not always be appropriate, particularly in cases where the anomaly being imaged is generated by a non-smooth spatial process. Timelapse imaging of flow-induced seismic velocity anomalies is one such case; flow features are often characterized by spatial compactness or connectivity. We develop a traveltime tomography algorithm which selects for compact solutions through application of model-space iteratively reweighted least squares. Our technique is an adaptation of minimum support regularization methods previously developed within the potential theory community. We emphasize the application of compactness constraints to timelapse datasets differenced in the data domain, a process which allows recovery of compact perturbations in model properties. We test our inversion algorithm on a simple synthetic dataset generated using a velocity model with several localized velocity anomalies. We then demonstrate the efficacy of the algorithm on a CO2 sequestration monitoring dataset acquired at the Frio pilot site. In both cases, the addition of compactness constraints improves image quality by reducing spatial smearing due to limited angular aperture in the acquisition geometry.Toksoz, M. NafiMassachusetts Institute of Technology. Earth Resources Laborator
Spreading of Persistent Infections in Heterogeneous Populations
Up to now, the effects of having heterogeneous networks of contacts have been
studied mostly for diseases which are not persistent in time, i.e., for
diseases where the infectious period can be considered very small compared to
the lifetime of an individual. Moreover, all these previous results have been
obtained for closed populations, where the number of individuals does not
change during the whole duration of the epidemics. Here, we go one step further
and analyze, both analytically and numerically, a radically different kind of
diseases: those that are persistent and can last for an individual's lifetime.
To be more specific, we particularize to the case of Tuberculosis' (TB)
infection dynamics, where the infection remains latent for a period of time
before showing up and spreading to other individuals. We introduce an
epidemiological model for TB-like persistent infections taking into account the
heterogeneity inherent to the population structure. This sort of dynamics
introduces new analytical and numerical challenges that we are able to sort
out. Our results show that also for persistent diseases the epidemic threshold
depends on the ratio of the first two moments of the degree distribution so
that it goes to zero in a class of scale-free networks when the system
approaches the thermodynamic limit.Comment: 12 pages and 2 figures. Revtex format. Submitted for publication
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Acquisition of time-lapse, 6-component, P- and S-wave, crosswell seismic survey with orbital vibrator and of time-lapse VSP for CO2 injection monitoring
Using an orbital vibrator source (2-components), and a 40 level 3-component geophone string, a 6-component crosswell survey was acquired before and after a CO2 injection in a saline aquifer. Decomposition of the two source components and component rotation of both source and sensors created good separation of P- and S-wave energy allowing independent analysis of travel time and reflectivity. A time-lapse VSP was also acquired
Mean-Field Interacting Boson Random Point Fields in Weak Harmonic Traps
A model of the mean-field interacting boson gas trapped by a weak harmonic
potential is considered by the \textit{boson random point fields} methods. We
prove that in the Weak Harmonic Trap (WHT) limit there are two phases
distinguished by the boson condensation and by a different behaviour of the
local particle density. For chemical potentials less than a certain critical
value, the resulting Random Point Field (RPF) coincides with the usual boson
RPF, which corresponds to a non-interacting (ideal) boson gas. For the chemical
potentials greater than the critical value, the boson RPF describes a divergent
(local) density, which is due to \textit{localization} of the macroscopic
number of condensed particles. Notice that it is this kind of transition that
observed in experiments producing the Bose-Einstein Condensation in traps
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